南京理工大学学报（自然科学版）2018，Vol.42Issue(3)：374-379,6.DOI:10.14177/j.cnki.32-1397n.2018.42.03.018
Caputo导数下分数阶Hamilton系统的Noether准对称性定理
Noether quasi-symmetry theorems for fractional Hamilton system in terms of Caputo derivatives
摘要
Abstract
The fractional conserved quantities and the Noether quasi-symmetry for a fractional Hamilton system in terms of Caputo derivatives are proposed and studied to explore the internal relation between symmetry and conserved quantities for non-conservative dynamical systems under fractional models. The definition and the criterion of Noether quasi-symmetry for the fractional Hamilton system in terms of Caputo derivatives are established. The Noether quasi-symmetry theorem is deduced by using the time-reparameterization method based on the concept of Frederico-Torres fractional conserved quantity. A fractional Hamilton system is taken as an example,and the quasi- symmetries of the system and corresponding fractional conserved quantities are given. The methods and results of this study are universal and can be extended to non-holonomic non-conservative dynamic systems,etc.关键词
Caputo 导数/分数阶Hamilton 系统/Noether 准对称性/非保守动力学系统/分数阶守恒量Key words
Caputo derivatives/fractional Hamilton system/Noether quasi-symmetry/non-conservative dynamical systems/fractional conserved quantities分类
数理科学引用本文复制引用
刘艳东,张毅..Caputo导数下分数阶Hamilton系统的Noether准对称性定理[J].南京理工大学学报（自然科学版）,2018,42(3):374-379,6.基金项目
国家自然科学基金(11572212 （）
11272227) （）
苏州科技大学研究生科研创新计划(SKYCX16_004) （SKYCX16_004）
